Final answer:
The total amount to repay is $1,500 and the company is charging an annual interest rate of approximately 1.597%. Hence the correct answer is option B
Step-by-step explanation:
To find the total amount you will repay, you need to find the number of $500 increments in the loan amount. Since $500 is equivalent to $30 a day, the loan amount can be divided by $500 to get the number of increments. In this case, $1,440 / $500 = 2.88 increments. Since you cannot have a fraction of an increment, round up to the nearest whole number, which is 3. Therefore, you will repay 3 increments of $500, which is $1,500.
To find the annual interest rate, you need to calculate the amount of interest paid over the loan period. Each increment of $500 incurs a daily interest cost of $30. Multiply this by the number of days in the loan period (276) to get the total interest paid: $30 * 276 = $8,280. Now, divide the total interest paid by the loan amount ($8,280 / $1,440) and multiply by 100 to get the interest rate as a percentage: (8280 / 1440) * 100 = 575%. Since the question assumes a 360-day year, divide the interest rate by 360 to get the annual interest rate: 575% / 360 = 1.597%.
Therefore, the company is actually charging an annual interest rate of approximately 1.597%.
Hence the correct answer is option B